1. Field of the Invention
The present invention relates to a numerical controller for a machining apparatus having three linear axes and at least two rotary axes for performing five-axis machining.
2. Description of Related Art
Described in U.S. Pat. No. 6,735,495 is a known arrangement for five-axis machining in which a conical surface or the like is machined by programming a movement path for a tool end point and specifying tool postures at a start point and an end point of the movement path.
FIGS. 11a and 11b are views illustrating the conical surface machining described in U.S. Pat. No. 6,735,495. FIG. 11a is a stereographic view, and FIG. 11b is a plan view taken from above FIG. 11a. In this machining, a path for a tool tip is designated by a circular arc, and tool posture vectors at a start point and an end point of the path are programmed as a start point vector and an end point vector, respectively. A first angle PHI on a plane that connects the starting and end point vectors (angle between the start point vector and a line as a projection of the tool posture vector on the vector connecting plane) and a second angle PSI of a tool posture vector perpendicular to the connecting plane are interpolated. By doing this, the conical surface can be machined in a manner such that the tool tip is moved along the programmed circular arc and that the tool posture on the conical surface is changed from the direction of the start point vector to that of the end point vector.
As shown in FIG. 12, moreover, a method is also described in which a conical surface is machined by interpolating a conical rotational angle around the central axis of the tool posture vector, which is given as the first angle PHI, and a conical tip angle as the second angle PSI. As shown in FIG. 13, furthermore, there is described a case where machining is performed for a noncircular bottom face along which the tool end point moves with those angles varied with respect to the conical surface by polynomial interpolation.
The arrangement described in U.S. Pat. No. 6,735,495 is based on the assumption that machining is performed on the conical surface or a surface varied with respect to it and that the start point vector, end point vector, and tool posture vector on the conical surface being interpolated, or their extensions cross one another at one point.
However, the given starting and end point vectors and the tool posture vector obtained by calculation are not always present on the same conical surface. In machining a surface having the shape shown in FIGS. 14a and 14b, for example, the method described in the aforementioned patent document cannot ensure interpolation.
FIG. 14a is a stereographic view, and FIG. 14b is a plan view taken from above FIG. 14a. In the example shown in FIGS. 14a and 14b, extensions of starting and end point vectors never cross each other. This is because the starting and end point vectors are not on a conical surface with a circular bottom face.